Bortezomib(Velcade (R))-Thalidomide-Dexamethasone (VTD) Is Superior to Thalidomide-Dexamethasone (TD) In Patients with Multiple Myeloma (MM) Progressing or Relapsing After Autologous Transplantation.

Introduction: The Thalidomide-Dexamethasone (TD) regimen has provided encouraging results in relapsed MM. To improve results, bortezomib (Velcade) has been added to the combination in previous phase II studies, the so called VTD regimen. In January 2006, the European Group for Blood and Marrow Transplantation (EBMT) and the Intergroupe Francophone du Myélome (IFM) initiated a prospective, randomized, parallel-group, open-label phase III, multicenter study, comparing VTD (arm A) with TD (arm B) for MM patients progressing or relapsing after autologous transplantation. Patients and Methods: Inclusion criteria: patients in first progression or relapse after at least one autologous transplantation, including those who had received bortezomib or thalidomide before transplant. Exclusion criteria: subjects with neuropathy above grade 1 or non secretory MM. Primary study end point was time to progression (TTP). Secondary end points included safety, response rate, progression-free survival (PFS) and overall survival (OS). Treatment was scheduled as follows: bortezomib 1.3 mg/m2 was given as an i.v bolus on Days 1, 4, 8 and 11 followed by a 10-Day rest period (days 12 to 21) for 8 cycles (6 months) and then on Days 1, 8, 15, 22 followed by a 20-Day rest period (days 23 to 42) for 4 cycles (6 months). In both arms, thalidomide was scheduled at 200 mg/Day orally for one year and dexamethasone 40 mg/Day orally four days every three weeks for one year. Patients reaching remission could proceed to a new stem cell harvest. However, transplantation, either autologous or allogeneic, could only be performed in patients who completed the planned one year treatment period. Response was assessed by EBMT criteria, with additional category of near complete remission (nCR). Adverse events were graded by the NCI-CTCAE, Version 3.0.The trial was based on a group sequential design, with 4 planned interim analyses and one final analysis that allowed stopping for efficacy as well as futility. The overall alpha and power were set equal to 0.025 and 0.90 respectively. The test for decision making was based on the comparison in terms of the ratio of the cause-specific hazards of relapse/progression, estimated in a Cox model stratified on the number of previous autologous transplantations. Relapse/progression cumulative incidence was estimated using the proper nonparametric estimator, the comparison was done by the Gray test. PFS and OS probabilities were estimated by the Kaplan-Meier curves, the comparison was performed by the Log-Rank test. An interim safety analysis was performed when the first hundred patients had been included. The safety committee recommended to continue the trial. Results: As of 1st July 2010, 269 patients had been enrolled in the study, 139 in France (IFM 2005-04 study), 21 in Italy, 38 in Germany, 19 in Switzerland (a SAKK study), 23 in Belgium, 8 in Austria, 8 in the Czech republic, 11 in Hungary, 1 in the UK and 1 in Israel. One hundred and sixty nine patients were males and 100 females; the median age was 61 yrs (range 29-76). One hundred and thirty six patients were randomized to receive VTD and 133 to receive TD. The current analysis is based on 246 patients (124 in arm A, 122 in arm B) included in the second interim analysis, carried out when 134 events were observed. Following this analysis, the trial was stopped because of significant superiority of VTD over TD. The remaining patients were too premature to contribute to the analysis. The number of previous autologous transplants was one in 63 vs 60 and two or more in 61 vs 62 patients in arm A vs B respectively. The median follow-up was 25 months. The median TTP was 20 months vs 15 months respectively in arm A and B, with cumulative incidence of relapse/progression at 2 years equal to 52% (95% CI: 42%-64%) vs 70% (95% CI: 61%-81%) (p=0.0004, Gray test). The same superiority of arm A was also observed when stratifying on the number of previous autologous transplantations. At 2 years, PFS was 39% (95% CI: 30%-51%) vs 23% (95% CI: 16%-34%) (A vs B, p=0.0006, Log-Rank test). OS in the first two years was comparable in the two groups. Conclusion: VTD resulted in significantly longer TTP and PFS in patients relapsing after ASCT. Analysis of response and safety data are on going and results will be presented at the meeting. Protocol EU-DRACT number: 2005-001628-35.

Clinical experience to date with nilotinib in gastrointestinal stromal tumors.

Nilotinib, a novel tyrosine kinase inhibitor (TKI) that inhibits BCR-ABL, the stem cell factor receptor (KIT), and platelet-derived growth factor receptor-alpha (PDGFRα), is approved for the treatment of patients with newly diagnosed Philadelphia chromosome-positive chronic myelogenous leukemia (CML) and those with CML that is imatinib-resistant or -intolerant. Due to its potent inhibition of KIT and PDGFRα--the two tyrosine kinases that are the central oncogenic mechanisms of gastrointestinal stromal tumors (GIST)--nilotinib also has been investigated for potential efficacy and safety in patients with GIST who have progressed on other approved treatments. Initial results have been encouraging, as nilotinib has demonstrated clinical efficacy and safety in a phase I trial as either a single agent or in combination with imatinib, as well as in heavily pretreated patients with GIST in a compassionate use program. In addition, the phase III trial of nilotinib versus best supportive care (with or without a TKI at the investigator's discretion) indicated that nilotinib may have efficacy in some third-line patients. Furthermore, the Evaluating Nilotinib Efficacy and Safety in Clinical Trials (ENEST g1 trial), a phase III randomized, open-label study comparing the safety and efficacy of imatinib versus nilotinib in the first-line treatment of patients with GIST, is currently under way. Other studies with nilotinib either have been initiated or are in development. Based on published and accruing clinical data, nilotinib shows potential as a new drug in the clinician's armamentarium for the management of GIST.

ß-Catenin Regulation during the Cell Cycle: Implications in G2/M and Apoptosis

ß-catenin is a multifunctional protein involved in cell-cell adhesion and Wnt signal transduction. ß-Catenin signaling has been proposed to act as inducer of cell proliferation in different tumors. However, in some developmental contexts and cell systems ß-catenin also acts as a positive modulator of apoptosis. To get additional insights into the role of ß-Catenin in the regulation of the cell cycle and apoptosis, we have analyzed the levels and subcellular localization of endogenous ß-catenin and its relation with adenomatous polyposis coli (APC) during the cell cycle in S-phase¿synchronized epithelial cells. ß-Catenin levels increase in S phase, reaching maximum accumulation at late G2/M and then abruptly decreasing as the cells enter into a new G1 phase. In parallel, an increased cytoplasmic and nuclear localization of ß-catenin and APC is observed during S and G2 phases. In addition, strong colocalization of APC with centrosomes, but not ß-catenin, is detected in M phase. Interestingly, overexpression of a stable form of ß-catenin, or inhibition of endogenous ß-catenin degradation, in epidermal keratinocyte cells induces a G2 cell cycle arrest and leads to apoptosis. These results support a role for ß-catenin in the control of cell cycle and apoptosis at G2/M in normal and transformed epidermal keratinocytes.

Targeting intratumoral B cells with rituximab in addition to CHOP in angioimmunoblastic T-cell lymphoma. A clinicobiological study of the GELA.

Background In angioimmunoblastic T-cell lymphoma, symptoms linked to B-lymphocyte activation are common, and variable numbers of CD20(+) large B-blasts, often infected by Epstein-Barr virus, are found in tumor tissues. We postulated that the disruption of putative B-T interactions and/or depletion of the Epstein-Barr virus reservoir by an anti-CD20 monoclonal antibody (rituximab) could improve the clinical outcome produced by conventional chemotherapy. DESIGN AND METHODS: Twenty-five newly diagnosed patients were treated, in a phase II study, with eight cycles of rituximab + chemotherapy (R-CHOP21). Tumor infiltration, B-blasts and Epstein-Barr virus status in tumor tissue and peripheral blood were fully characterized at diagnosis and were correlated with clinical outcome. RESULTS: A complete response rate of 44% (95% CI, 24% to 65%) was observed. With a median follow-up of 24 months, the 2-year progression-free survival rate was 42% (95% CI, 22% to 61%) and overall survival rate was 62% (95% CI, 40% to 78%). The presence of Epstein-Barr virus DNA in peripheral blood mononuclear cells (14/21 patients) correlated with Epstein-Barr virus score in lymph nodes (P<0.004) and the detection of circulating tumor cells (P=0.0019). Despite peripheral Epstein-Barr virus clearance after treatment, the viral load at diagnosis (>100 copy/μg DNA) was associated with shorter progression-free survival (P=0.06). Conclusions We report here the results of the first clinical trial targeting both the neoplastic T cells and the microenvironment-associated CD20(+) B lymphocytes in angioimmunoblastic T-cell lymphoma, showing no clear benefit of adding rituximab to conventional chemotherapy. A strong relationship, not previously described, between circulating Epstein-Barr virus and circulating tumor cells is highlighted.

Dimensional reduction and gauge group reduction in Bianchi-type cosmology

In this paper we examine in detail the implementation, with its associated difficulties, of the Killing conditions and gauge fixing into the variational principle formulation of Bianchi-type cosmologies. We address problems raised in the literature concerning the Lagrangian and the Hamiltonian formulations: We prove their equivalence, make clear the role of the homogeneity preserving diffeomorphisms in the phase space approach, and show that the number of physical degrees of freedom is the same in the Hamiltonian and Lagrangian formulations. Residual gauge transformations play an important role in our approach, and we suggest that Poincaré transformations for special relativistic systems can be understood as residual gauge transformations. In the Appendixes, we give the general computation of the equations of motion and the Lagrangian for any Bianchi-type vacuum metric and for spatially homogeneous Maxwell fields in a nondynamical background (with zero currents). We also illustrate our counting of degrees of freedom in an appendix.

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Diracs method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

hMMP9 as predictive factor for response and progression free survival in breast cancer patients treated with bevacizumab and pegylated liposomal doxorubicin (PLD)

Background: The anti-angiogenic drug, bevacizumab (Bv), is currently used in the treatment of different malignancies including breast cancer. Many angiogenesis-associated molecules are found in the circulation of cancer patients. Until now, there are no prognostic or predictive factors identified in breast cancer patients treated with Bv. We present here the first results of the prospective monitoring of 6 angiogenesis-related molecules in the peripheral blood of breast cancer patients treated with a combination of Bv and PLD in the phase II trial, SAKK 24/06. Methods: Patients were treated with PLD (20 mg/m2) and Bv (10 mg/kg) on days 1 and 15 of each 4-week cycle for a maximum of 6 cycles, followed by Bv monotherapy maintenance (10 mg/m2 q2 weeks) until progression or severe toxicity. Plasma and serum samples were collected at baseline, after 2 months of therapy, then every 3 months and at treatment discontinuation. Enzyme-linked immunosorbent assays (Quantikine, R&D Systems and Reliatech) were used to measure the expression levels of human vascular endothelial growth factor (hVEGF), placental growth factor (hPlGF), matrix metalloproteinase 9 (hMMP9) and soluble VEGF receptors hsVEGFR-1, hsVEGFR-2 and hsVEGFR-3. The log-transformed data (to reduce the skewness) for each marker was analyzed using an analysis of variance (ANOVA) model to determine if there was a difference between the mean of the subgroups of interest (where α = 0.05). The untransformed data was also analyzed in the same manner as a "sensitivity" check. Results: 132 blood samples were collected in 41 out of 43 enrolled patients. Baseline levels of the molecules were compared to disease status according to RECIST. There was a statistically significant difference in the mean of the log-transformed levels of hMMP9 between responders [CR+PR] versus the mean in patients with PD (p-value=0.0004, log fold change=0.7536), and between patients with disease control [CR+PR+SD] and those with PD (p-value=<0.0001, log fold change=0.81559), with the log-transformed level of hMMP9 being higher for the responder group. The mean of the log-transformed levels of hsVEGFR-1 was statistically significantly different between patients with disease control [CR+PR+SD] and those with PD (p-value=0.0068, log fold change=-0.6089), where the log-transformed level of hsVEGFR-1 was lower for the responder group. The log-transformed level of hMMP9 at baseline was identified as a significant prognostic factor in terms of progression free survival (PFS): p-value=0.0417, hazard ratio (HR)=0.574 with a corresponding 95% confidence interval (0.336 - 0.979)). No strong correlation was shown either between the log-transformed levels of hsVEGF, hPlGF, hsVEGFR-2 or hsVEGFR-3 and clinical response or the occurrence of severe toxicity, or between the levels of the different molecules. Conclusions: Our results suggest that baseline plasma level of the matrix metalloproteinase, hMMP9, could predict tumor response and PFS in patients treated with a combination of Bv and PLD. These data justify further investigation in breast cancer patients treated with anti-angiogenic therapy.

Influence of disorder strength on phase-field models of interfacial growth

We study the influence of disorder strength on the interface roughening process in a phase-field model with locally conserved dynamics. We consider two cases where the mobility coefficient multiplying the locally conserved current is either constant throughout the system (the two-sided model) or becomes zero in the phase into which the interface advances (one-sided model). In the limit of weak disorder, both models are completely equivalent and can reproduce the physical process of a fluid diffusively invading a porous media, where super-rough scaling of the interface fluctuations occurs. On the other hand, increasing disorder causes the scaling properties to change to intrinsic anomalous scaling. In the limit of strong disorder this behavior prevails for the one-sided model, whereas for the two-sided case, nucleation of domains in front of the invading front are observed.

Rationale for consolidation to improve progression-free survival in patients with non-Hodgkin's lymphoma: a review of the evidence.

Non-Hodgkin's lymphoma (NHL) comprises both indolent forms, including follicular lymphoma (FL) and marginal zone lymphoma (MZL), and aggressive forms, including diffuse large B-cell lymphoma (DLBCL) and mantle cell lymphoma (MCL). FL and DLBCL are the most common subtypes of indolent and aggressive NHL, respectively. Although these lymphomas exhibit different clinical behaviors and outcomes, the prognosis is negatively affected in both DLBCL and FL by the lack of a complete response (CR) with standard treatment options. The aim of therapy should therefore be achievement of a CR, which is not only associated with longer progression-free survival (PFS) and overall survival times, but is also a prerequisite for a cure, particularly in DLBCL. Consolidation treatment with radioimmunotherapy (RIT) is an innovative treatment approach to increase CR rates. Phase II studies have indicated promising results with yttrium-90 ((90)Y)-ibritumomab tiuxetan and iodine-131 ((131)I)-tositumomab as consolidation following induction therapy for previously untreated patients with advanced FL. More recently, investigators reported a marked increase in CR rates and significant improvements in PFS using standard chemotherapy regimens followed by (90)Y-ibritumomab tiuxetan in a phase III randomized trial in patients with previously untreated FL. Data also suggest that RIT may play a role in the treatment of high-risk DLBCL, with encouraging PFS results from a phase II trial of (90)Y-ibritumomab tiuxetan consolidation following induction with rituximab plus chemotherapy in elderly patients with previously untreated DLBCL. With the higher CR rates and longer PFS times observed in patients with FL and DLBCL, as well as encouraging early data from MZL and MCL consolidation trials, RIT appears to have an important role in the treatment of patients with NHL.

Manganese accumulation and its relation to "eucalyptus shoot blight in the Vale do Rio Doce"

Eucalyptus Shoot Blight in the Vale do Rio Doce (ESBVRD) is an anomaly that leads to reduced growth and, in more extreme cases, to death of eucalyptus plants. Initially diagnosed in plantations in the region of the Vale do Rio Doce, in the State of Minas Gerais, Brazil, this problem has also been found in plantations in other regions of the country and even in other countries. Although the symptoms of this anomaly are well-known, its causes are not yet understood. The aim of this study was to evaluate the cause-effect relationship between accumulation of manganese (Mn) in eucalyptus clones and ESBVRD. Characterization of the environment in areas of greater occurrence of this problem in regard to soil, climate and fluctuation of the water table was undertaken in eucalyptus plantations of the Celulose Nipo-brasileira S.A. (Cenibra) company in the region of the Vale do Rio Doce. Plant tissues were sampled in two situations. In the first situation, diagnosis occurred in the initial phase of the anomaly in clones with differentiated tolerance to the problem; in the second situation, diagnosis was made in a single clone, considered to be sensitive, in two time periods - in the phase with the strong presence of symptoms and in the recovery phase, in areas of occurrence and in areas of escape from the problem. The most ESBVRD-sensitive clone showed much higher (4.8 times higher) leaf Mn contents than more tolerant clones. In plants with the anomaly, Mn leaf contents were greater than 3,070 mg kg-1, much greater than the quantity found in those without the anomaly (734 mg kg-1). In the period in which the symptoms began to wane, there was a sharp decline in leaf Mn contents, from 2,194 to 847 mg kg-1. Manganese content in the above ground part and plant litter (44.4 g ha-1) in the area of occurrence of the anomaly was three times greater than that found in these same components (14.1 g ha-1) in the area of absence of the symptom. Based on the evidence found, such as the existence of environmental conditions favorable to high Mn availability to the plants in the areas of greatest incidence of ESBVRD, greater uptake of Mn in sensitive clones and in plants with symptoms, and a synchronism between the intensity of symptoms of ESBVRD and leaf Mn contents, it may be inferred that temporary excess of Mn in eucalyptus plants is closely related to ESBVRD.

Impact of HLA A2 and cytomegalovirus serostatus on outcomes in patients with leukemia following matched-sibling myeloablative allogeneic hematopoietic cell transplantation.

BACKGROUND AND OBJECTIVES: Donor cytomegalovirus seropositivity was reported to improve leukemia outcomes in HLA-A2 identical hematopoietic cell transplant (HCT) recipients, due to a possible cross-reactivity of donor HLA-A2-restricted CMV-specific T cells with minor histocompatibility (H) antigen of recipient cells. This study analyzed the role of donor CMV serostatus and HLA-A2 status on leukemia outcomes in a large population of HLA-identical HCT recipients. DESIGN AND METHODS: Leukemia patients transplanted between 1992 and 2003 at the Fred Hutchinson Cancer Research Center were categorized as standard risk [leukemia first remission, chronic myeloid leukemia in chronic phase (CML-CP)] and high risk (advanced disease) patients. Time-to-event analysis was used to evaluate the risk of relapse and death associated with HLA-A2 status and donor CMV serostatus. RESULTS: In standard risk patients, acute leukemia (p<0.001) and sex mismatch (female to male, p=0.004)) independently increased the risk of death, while acute leukemia increased the risk of relapse (p<0.001). In high risk patients acute leukemia (p=0.01), recipient age > or = 40 (p=0.005) and herpes simplex virus (HSV) seropositivity (p<0.001) significantly increased the risk death; HSV seropositivity (p=0.006) increased the risk of relapse. Donor CMV serostatus had no significant effect on mortality or relapse in any HLA group. INTERPRETATION AND CONCLUSION: This epidemiological study did not confirm the previously reported effect of donor CMV serostatus on the outcomes of leukemia in HLA-A2-identical HCT recipients. Addressing the question of cross-reactivity of HLA-A2-restricted CMV-specific T cells with minor H antigens in a clinical study would require knowledge of the patient's minor H antigen genotype. However, because of the unbalanced distribution of HLA-A2-restricted minor H antigens in the population and their incomplete identification, this question might be more appropriately evaluated in in vitro experiments than in a clinical study.

Self-Consolidating Concrete—Applications for Slip-Form Paving: Phase II, May 2011

The goal of the project was to develop a new type of self-consolidating concrete (SCC) for slip-form paving to simplify construction an make smoother pavements. Developing the new SCC involved two phases: a feasibility study (Phase I sponsored by TPF-5[098] and concrete admixtures industry) and an in-depth mix proportioning and performance study and field applications (Phase II). The phase I study demonstrated that the new type of SCC needs to possess not only excellent self-consolidating ability before a pavement slab is extruded, but also sufficient “green” strength (the strength of the concrete in a plastic state) after the extrusion. To meet these performance criteria, the new type of SCC mixtures should not be as fluid as conventional SCC but just flowable enough to be self-consolidating. That is, this new type of SCC should be semi-flowable self-consolidating concrete (SFSCC). In the phase II study, effects of different materials and admixtures on rheology, especially the thixotropy, and green strength of fresh SFSCC have been further investigated. The results indicate that SFSCC can be designed to (1) be workable enough for machine placement, (2) be self-consolidating without segregation, (3) hold its shape after extrusion from a paver, and (4) have performance properties (strength and durability) comparable with current pavement concrete. Due to the combined flowability (for self-consolidation) and shape-holding ability (for slip-forming) requirements, SFSCC demands higher cementitious content than conventional pavement concrete. Generally, high cementitious content is associated with high drying shrinkage potential of the concrete. However, well-proportioned and well-constructed SFSCC in a bike path constructed at Ames, IA, has not shown any shrinkage cracks after approximately 3 years of field service. On the other hand, another SFSCC pavement with different mix proportions and construction conditions showed random cracking. The results from the field SFSCC performance monitoring implied that not only the mix proportioning method but also the construction practice is important for producing durable SFSCC pavements. A carbon footprint, energy consumption, and cost analysis conducted in this study have suggested that SFSCC is economically comparable to conventional pavement concrete in fixed-form paving construction, with the benefit of faster, quieter, and easier construction.

Premature epiphyseal closure in an adolescent treated by retinoids for acne: An unusual cause of anterior knee pain

Introduction.- Retinoids are effective and widely used for the treatment of severe acne. Their use can be, however, associated with numerous side effects. For example, some rare cases of premature epiphyseal closure were reported.Observation.- A sixteen-year-old soccer player consulted for bilateral progressive anterior knee pain, since two months, evoking a femoro-patellar origin. After physiotherapy, the pain decreases on the right but remained on the left. The history taking brought out the use of isotretinoin for more than 6 months (0.5 mg/kg). Magnetic resonance imaging (MRI) findings showed an irregularity of the growth plate and an important metaphyso-epiphyseal oedema, more marked on the left. The diagnosis of retinoid induced premature ephysieal closure was retained. The treatment was stopped, with a resolution of symptoms within two months. The control MRI of the left knee present persisting small sequelar thumbprint-like growth plate lesion. Eighteen months later, neither limb-length discrepancy nor static disorder was noticed.Discussion.- Premature epiphyseal closure is a rare complication of retinoid treatment of acne. Retinoids induce an invasion of the growth plate by osteoclasts and a decrease in proteoglycans synthesis. The knee seems the most involved joint. The clinical presentation is aspecific, sometimes lightly symptomatic. A careful pharmacological history and an appropriate imaging are necessary. MRI is now the gold standard. It shows an irregularity of the growth plate with an oedema on both sides. In chronic phase, a thumbprint-like image may persist. The symptoms resolution arises in few weeks after the treatment interruption. A single case of static disorder was reported until now. The small size of the growth plate interruptions, insufficient to lead to a growth disorder if the medicament is stopped early enough, explains probably it. This complication being rare, a radiological follow-up of the young patients treated by retinoids is not proposed.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.